Question

The work done in slowly lifting a body from earth's surface to a height R (radius of earth) is equal to two times the work done in lifting the same body from earth's surface to a height h. Here h is equal to

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Work done = increase in gravitational potential energy

$\therefore$ $W_1=\frac{mgR}{1+\frac{R}{R}}=\frac{mgR}{2}$ $(△U=\frac{mgh}{1+\frac{h}{R}})$

and $W_2=\frac{mgh}{1+\frac{h}{R}}$

Given that $W_1=2W_2$

or $\frac{mgR}{2}=\frac{2mgh}{1+\frac{h}{R}}$ or $h=\frac{R}{3}$